When the system is at equilibrium for the given chemical reaction:
[tex]\[ 2 \text{CH}_4(g) \leftrightarrow \text{C}_2\text{H}_2(g) + 3 \text{H}_2(g) \][/tex]
several important aspects must be considered:
### Concentrations:
1. Concentration Constancy: The concentrations of the reactants ([tex]\(\text{CH}_4\)[/tex]) and the products ([tex]\(\text{C}_2\text{H}_2\)[/tex] and [tex]\(\text{H}_2\)[/tex]) remain constant over time. This means that the amounts of [tex]\(\text{CH}_4\)[/tex], [tex]\(\text{C}_2\text{H}_2\)[/tex], and [tex]\(\text{H}_2\)[/tex] in the system do not change as the system is at equilibrium.
### Reactions Occurring:
2. Forward Reaction: The reaction where 2 methane molecules ([tex]\(2 \text{CH}_4\)[/tex]) are converted into one acetylene molecule ([tex]\(\text{C}_2\text{H}_2\)[/tex]) and three hydrogen molecules ([tex]\(3 \text{H}_2\)[/tex]):
[tex]\[ 2 \text{CH}_4 \rightarrow \text{C}_2\text{H}_2 + 3 \text{H}_2 \][/tex]
3. Backward Reaction: Simultaneously, the reverse reaction also occurs where one acetylene molecule ([tex]\(\text{C}_2\text{H}_2\)[/tex]) and three hydrogen molecules ([tex]\(3 \text{H}_2\)[/tex]) are converted back into two methane molecules ([tex]\(2 \text{CH}_4\)[/tex]):
[tex]\[ \text{C}_2\text{H}_2 + 3 \text{H}_2 \rightarrow 2 \text{CH}_4 \][/tex]
### Reaction Rates:
4. Equal Rates: At equilibrium, the rate of the forward reaction (conversion of [tex]\(\text{CH}_4\)[/tex] to [tex]\(\text{C}_2\text{H}_2\)[/tex] and [tex]\(\text{H}_2\)[/tex]) is equal to the rate of the backward reaction (conversion of [tex]\(\text{C}_2\text{H}_2\)[/tex] and [tex]\(\text{H}_2\)[/tex] back to [tex]\(\text{CH}_4\)[/tex]). This balance ensures that there is no net change in the concentrations of the reactants or products over time.
In summary, at equilibrium, the concentrations of methane ([tex]\(\text{CH}_4\)[/tex]), acetylene ([tex]\(\text{C}_2\text{H}_2\)[/tex]), and hydrogen ([tex]\(\text{H}_2\)[/tex]) remain constant. Both the forward and backward reactions are occurring simultaneously with equal rates, ensuring that the system remains in a state of dynamic equilibrium.
